What causes time dilation in gravitational fields?

[harrylin]

[...]
You may counter by saying that there is a difference between true gravity and the pseudo-gravity of acceleration, but that difference is a second-order tidal effect, whereas gravitational time dilation is first order effect and the dominant term (especially for extremely large black holes).

The equivalence principle served its purpose, but many clues help us to distinguish between gravitation and acceleration (even looking out of the window!). If we follow the reasoning that we should ignore the clues that we receive from small effects, then we should prefer Newton's theory.

 

[Quickless]

Time is invariant with respect to regime. It is not time that is changing but the measurement of time. Consideration should be given to whether time is a thing in and of itself or just a measurement.

 

[pervect]

I've been a bit distracted by other things recently, but there was one thing I thought of that I did want to mention.

That is , if you consider "Einstein's elevator", it's widely recognized that there's a "gravitional field" in the eleveator's frame (if it's small enough), or in the elevator's Fermi-normal coordinates (if the elevator is a bit too large to have a frame we replace the frame with the fermi-coordinates0.

So the clock "higher" in the elevator ticks faster. We might also say that the Rindler metric describes the space-time of the elevator, and that the time dilation is described by g_00 of that metric.

However, it is a definite error to imagine that this gravitational time dilation effect exists in the inertial frame which also exists and can be used to describe the elevator's motion.

The Rindler metric has g_00 vary with position, but the Minkowskii metric of flat space-time has a constant g_00.

In the inertial frame, there is absolutely no gravity field,and absolutely no gravitational time dilation,either. (But there is the usual relativistic doppler shift in the inertial frame, which is sufficient to explain allthe observed reception and transmission times. However, we can't say that one clock ticks faster or slower in said inertial frame, though we can say that there are doppler shifts, red shifts for light signals traveling from back-front for instance.

So, it's fairly easy to show that a simple change of coordinates or viewpoint causes "gravitational time dilation" , considered in isolation, to either appear or dissapear. In other words, gravitational time dilation is not a geomoetric object or tensor, it's just a piece of one.

So, that's one last reason why NOT to think of g_00 as "time slowing down". It's too simplistic, when you consider the whole picture, it's part of something bigger. The metric coefficeints depend on what coordinate systems one uses.